Barnard’s Star and the ‘Wait Equation’

by Paul Gilster on November 24, 2006

When do you decide to launch a starship? It’s a question based as much on cultural assumptions as technology. Start with the premise that we can ratchet up today’s velocities to 150 kilometers per second, roughly ten times the speed at which New Horizons will cross Pluto’s orbit. If we want to send a probe six light years to Barnard’s Star at that speed, we would be looking at a travel time of 12,000 years. That’s a lot of time, but better than Voyager’s 70,000-year plus travel time to the Centauri stars (if either Voyager were pointed in their direction).

Clearly, 12,000 years is too many, especially in an age that regards maximum mission time as the lifetime of a researcher working on the project. Besides, if we did launch that kind of mission, it would inevitably be passed enroute by a faster spacecraft. And that’s the conundrum: does there ever come a time when you do launch, or are you always waiting for better propulsion systems and faster travel times?

As Andrew Kennedy discovers in a paper we have just been discussing, there is indeed an optimum time, though one with a twist. Kennedy works with a doubling equation to describe how growth affects velocity of travel. From the paper:

If technology growth is likely to double every 100 years the speed at which this journey could be made, then…it would seem that a voyager need only wait 690 years or so to make the journey in 100 years or less (i.e. at a speed of 6/100 the speed of light). In other words, the star could be reached in well under a thousand years from now simply by waiting. Total time to destination is 690 years of wait + 100 years of travel = 790 years.

Barring unexpected breakthroughs, then, we get to Barnard’s star in roughly 800 years. Or should we wait even longer to launch as better technologies continue to emerge? Now it gets interesting: assuming continuous growth without such breakthroughs, there also comes a time when although growth continues to produce higher speeds, the waiting time for that growth is too long to make up the velocity difference.

After that minimum, the ship that leaves later arrives later. No getting to Barnard’s Star only to be greeted by those who launched a century after you did and got there first. Here’s Kennedy again, on a launch strategy for future mission directors:

If the civilisation has the capability to make several launches, then they could make use of the spread of arrival times to encourage individuals to leave on the basis that others would either be there first to welcome them or be following close behind bringing with them the future technologies.

And again:

…the wait calculation is crucial. Either side of the minimum, voyagers will arrive later than those who set off at the minimum. At the minimum wait time, growth will not catch the voyagers up during their journey. They will arrive to an unsettled destination, expecting others to follow, but not knowing if the vanguard of civilisation will appear on their horizon before much time has passed. If they leave before or after the minimum and find their destination still unsettled when they arrive, they will know that growth has slowed or stopped and that they will be alone for some time.

This is a rich paper that weaves economic growth patterns with the pace of technology over time and takes a sober look at how our culture might adapt to the possibilities of long-term missions. I wrote in a 2004 entry about van Vogt’s classic “Far Centaurus” story (Astounding, Jan. 1944) as an example of travelers being caught by faster technologies, but there are a number of related scenarios that science fiction writers could mine by pondering the equations in this paper. I was also interested to learn in an e-mail from Kennedy that he has a second paper on the subject in the works. We’ll look at it here when it appears.

This is the key assumption, and it is wrong. The doubling time for technology growth is itself accelerating. Technology growth doubled several times in the last 100 years, and now doubles about every 10 to 15 years or so, getting shorter every year. By 2025, that doubling time will be down around 2 years, and by 2030 should be down around a few weeks. Then things start to get interesting, when the doubling of technology growth occurs in a matter of days, or hours. At that point we reach the Singularity, beyond which no prediction of future technology is possible.

Even with Moore’s Law in the early days there was some expectation that it was not unending. Eventually, it was thought, a time would come when the curve would flatten by limits imposed by either practical techniques or physical laws. The time when this was predicted to occur had to be frequently revised. Of course that doesn’t mean the curve won’t flatten but fewer folks are willing to go out on a limb and make a firm prediction.

So, just how far can we confidently predict geometric “technology growth” with respect to interstellar travel? I have no idea. My own view is that meaningful (i.e. both economic and practical) progress will be gated on new and massive, not terribly predictable as of now, energy sources. In other words I’m doubtful, but could never prove, that technological improvements of known energy sources and using future propulsion methods will get us to the stars cheaply and quickly. I would like to be proven wrong.

Regarding long-term planning…I don’t see that happening any time soon. If we do decide it makes sense to wait a few centuries for better/faster/cheaper travel, that is equivalent, to me (here and now) to a decision to do nothing. That is, my decision to put off travel to a time after my death is not the same as long-term planning. Those not yet born won’t care about my decision. Theirs will be independent of any choice I make. True long-term planning would connect the two events. We don’t have that possibility, yet.

Another way of saying it, our available choices, today, are to do nothing or to make the travel attempt. If our effort to launch a craft is superceded by a future generation, I won’t know about. I’ll only know that I did something. This is a bit like the ancient (biblical?) story of the old man who planted a fig tree getting perplexed looks from his neighbors since it wouldn’t bear fruit for many decades and so the old man could never see the beneficial results. Modernizing the story, plant the tree today and in 25 years we could be manufacturing figs in a factory, and our grandchildren will laugh at the idea of planting a tree and waiting years for it to bear fruit. But what choice do we have today if we want to bequeath figs on our children?

Let me quote Kennedy’s last paragraph, which bears on what Ed says above:

“It is considered that the overall growth curve represents a summation of many inter-related sectors of growth, and that the probability of a discovery in any one sector contributing, on its own, to a sudden radical departure from the overall rate is not likely. While unpredictable changes can contribute to the overall growth rate, it would be wrong for interstellar voyagers to delay a departure based on the hope that a technological breakthrough will improve the journey times calculated on the basis of the known growth rate, and that to ignore the positive incentive described by the wait equation would be irrational.”

In other words, Kennedy sets out to describe an achievable ‘travel of velocity’ based on continuous growth, and he implies that growth is in general much flatter than some would suggest. I have no strong argument for or against the Singularity hypothesis myself, other than to say that the future is rarely so predictable even in the short term, and I frankly doubt that we will see the radical kinds of growth Ed mentions by 2030, but I suppose we’ll find out soon enough.

Re Ron’s comment: “If our effort to launch a craft is superceded by a future generation, I won’t know about. I’ll only know that I did something.” Agreed absolutely! And I love the fig analogy.

The logical choice seems to not wait at all. Every technology needs extensive testing for validation and further improvement. And the best way for a longterm test of an interstellar drive seems to be by sending it into interstellar space. For robotic probes the ultimate travel time is after all not a real concern. When the first probes have successfully reached their target and and if of course a system of sufficient interest (preferable with earth like planets) has been discovered in the vicinity of our own system, we can begin to talk about human travel.

Although exploring stars beyond our solar playground is fascinating, I think it would be better for us to focus on our own system (colonizing it) before attempting to explore others…at least until we have “faster than light travel.”

If the civilisation has the capability to make several launches, then they could make use of the spread of arrival times to encourage individuals to leave on the basis that others would either be there first to welcome them or be following close behind bringing with them the future technologies.

Assuming that there will BE follow-on missions. It might be prudent for each mission to assume they’re ‘it’.

Darnell ClaytonAlthough exploring stars beyond our solar playground is fascinating, I think it would be better for us to focus on our own system (colonizing it) before attempting to explore others…at least until we have “faster than light travel.”

You’ll hear the same argument from people determined that we not colonize the solar system.

We’ll do it as soon as practical and for the same reasons – because it’s possible and because we can afford to do it.

“This is the key assumption, and it is wrong. The doubling time for technology growth is itself accelerating. Technology growth doubled several times in the last 100 years, and now doubles about every 10 to 15 years or so, getting shorter every year. By 2025, that doubling time will be down around 2 years, and by 2030 should be down around a few weeks.”

Yes the assumption IS wrong.
Using an equally flawed growth analogy, my grandaughter will be over 10 feet tall before she is 10 years old.
We know nothing scientific about the laws (sic) governing the rate of technological innovation, saturation limits, and alleged singularities, however trendy with the geek elite.

Concerning the concept of accelerated “doubling” of technology I tend to disagree with it. My own perception (simply a perception and no I can’t rigerously defend it) is that technology reaches a plateau, areas diverge into subsets, then there is a rapid advancement due to positive feedback from the new, diverse areas. The advancement can give the impression of accelerating at an exponential rate but I would be leery of pinning it to a set rate of doubling in x time. Those subsets could simply dead end or further diverge, after research, into addtional subsets.

Currently many new fields are being followed and others are being discovered. I consider our current tech level to be at a plateau and in the refining stage. My own best guesstimate (of course that word exists, I used it didn’t I :) is that the next major blossoming is around 2015~2020. Some interesting things should occur.

I do not see any seriouse attempts at insterstellar exploration until we, as a species, are permanently established in space. That does not include the abortive, partial posterior thing currently in orbit. When we have people full time off planet, gathering resources off earth, then I think we’ll see efforts to reach the nearer stars. For an undertaking such as described either you must get the general populace excited about the concept to support such a costly undertaking or wait until tech and resource availability make the effort far less onerous. I do hope I’m still above ground to see it finally happen though.

Barnard’s star is moving towards its closest approach to Sol quite quickly reaching just 3.1 ly in 9700 AD (I think… been a while since I read the literature) so we might find it easier to wait anyway? Once we’re immortal and happy to let the stars dance to their own rhythm, that is.

Adam is right; Barnard’s Star is headed our way, and fast. My reference says 87 miles per second, closing to within four light years around 10,000 AD, but either way it’s a close approach! We can send Ray Kurzweil out to look at it…

Let’s see… 7,700 years to go 3.1 ly would take an average speed of (if my rapid calculator work is not in error) 39 km/s. Of course that’s a fly by at the rendezvous point. It would take a little more effort to achieve orbit – acceleration far from Earth.

If we delay 100 years to develop long-lasting instrumentation it only costs us another 1/2 km/s. No point in sending a dead metal box.

…both papers are downloadable. The 1999 article is more detailed and extrapolates back into the past quite a ways. The nearest encounter will be in 1.36 million years by Gl 710 at 1.1 ly (0.336 psc +/- 0.161 psc.) This will significantly perturb the Oort cloud and produce a comet shower 1.6 million years or so later. So c. 3 million AD we could be facing a Chixulub-style impactor hazard.

Ron’s got a point: “If we delay 100 years to develop long-lasting instrumentation it only costs us another 1/2 km/s. No point in sending a dead metal box.”

Figure a Barnard’s Star mission launching in 100 years with survivable instrumentation and a travel time of 7700 years. Sure, we’re not going to fly that mission, but it’s interesting that we can begin to sketch in the parameters of what could be done with just a slight bump in today’s technologies. We’re setting up the outer envelope of the possible; now to start figuring out how to shave a few millennia off that travel time.

Though we don’t have diamond filament yet I personally think we can get 1500 km/s in the near-term using ultra-light solar-sails on solar ‘fry-by’ launch trajectories. Thus only 200 years/light-year. At least Greg Matloff thinks it’s close to doable.

I like those numbers, Adam, and Matloff is always looking at ways to extend current technology — he doesn’t wait for exotic breakthroughs but tries to see what we can come up with in a reasonable amount of time. Which reminds me that I have a JBIS paper of his on solar sails that I want to discuss here soon.

Re Brian’s comment: “Assuming that there will BE follow-on missions. It might be prudent for each mission to assume they’re ‘it’.” A good point indeed, at least given our near-term history with Apollo!

The technologies will be like (?) in 9000 yrs from now, so waiting is indeed a best solution. However, we wont be alive in this period so it doesnt matter if we send one or wait until we all leave this world.

Consider Moore’s Law for computers for a moment. In 1982, i ran a computation on a $100,000 machine for a year. Were i to run this again on my 3 year old $400 home computer, it would take less than 2 hours. So, from my perspective, i’m encouraged to wait. But if i hadn’t written the code and tested it, i would not have learned anything back then. Also, waiting for faster hardware only works for me because i’m not creating the hardware.

So, why buy computer hardware at all? I mean, if it’s just going to be faster next year, why not wait? If everyone did this, the sales that drive the technology would collapse, and the technology advancement would halt. It turns out that you have to build the slower stuff today to be able to build the faster stuff tomorrow.

For interstellar travel, we aren’t talking about me waiting, we’re talking about all of humanity waiting. But if we wait without development, testing, etc., then the technology doesn’t have to advance. Now, we might be able to use carbon nanotube wires that were developed for communications and space elevators to make a really good solar sail. We might be able to adapt other technologies too. But if it turned out that what we really needed was an Orion drive (explode nukes behind you), the only way to do that is to do it. We’re not going to get it by waiting for some domestic need to develop it.

We need nearby goals. The Voyagers are headed out of the solar system. They were designed to get to Neptune. They’ve made it to the heleosheath. That’s a cool goal, reachable without being passed.

BTW, when will New Horizons pass Voyager I in distance from the Sun? I mean, we all heard that New Horizons was launched on a really fast rocket, and passed the Moon in 9 hours, and all that.

Never. Voyager I got a bigger gravity boost from Jupiter than New Horizons will get. New Horizons will never be as fast as Voyager I. That’s the breaks.

We still have minor planets and kuiper belt objects to fly to and study. Then there’s the big telescope project – where you send a probe out far enough to be able to use the Sun as a lens. That’s like 500 AU (or is it 1500 AU?).

As some have mentioned, the movement of the nearby stars makes a difference. Epsilon Eridani is coming our way, and others. You have to aim to where these things will be. Sometimes, waiting for close approach will cut down on time.

I’m optimistic that humans will send probes to interstellar distances. Eventually, humans will go interstellar distances. It’d be nice to get Earth life out to infect other galaxy clusters, before these fall off the light horizon forever.

I think our next goal will be the second focus point in our solar system which is around 550 AU from the sun (?). I assume that we have fusion propulsion around 2050 and it will take less than a year for a spacecraft reaching this point, if we extend the technology to its maximum limit.

I think sending a probe to the nearest star will start in the late 22th century when we have enough anti-matter for the trip. Well, it seems like i’m a day dreamer.

If you can launch a neutrino detector into space, the solar focal point will be closer than 550 AU, due to focusing by the dense solar core (the neutrinos pass through the outside of the sun without scattering, although there would be oscillation). At the focus the neutrinos intensity would be considerably amplified because that point would form a caustic (many nearby trajectories would focus to near the same point). This is unlike focusing of light around the sun.

I ran into this blog just recently. Even though the originator did email me shortly after my paper was published, this discussion wasn’t on the page then.

Almost everyone in this thread seems to missed the point, or at least if they did get it they are not talking about it.

I was explaining that given any kind of systematic growth (and yes, I do include calculations based on accelerating rates of growth) you can calculate how long to wait to achieve any particular goal in the quickest time. I am not talking about the ‘Columbus fallacy’. I go on to say that this calculation may well be crucial in the race between competing groups to colonize a particular world. Leave at the wrong time and you’ll end up last in the race. This is not going to be an insignificant consideration when the vast investment required to get to any interstellar destination will need to produce a payoff.

I also talk about growth rates and say that the world’s overall growth rate is a) surprisingly resilient to catastrophe, b) does not produce extraordinary innovations that alter the growth rate since the innovations are a function of the growth rate and not something apart.

Of course, the question of whether there is any attainable destination that will actually help us out in the hunt for resources is another issue.

andrew kennedy,thank you for your above interesting comments. i think you will find,as have i that this site is one of the most interesting i have found thus far! quite naturally as i think you imply,the trouble is that the destinations are indeed quite far away! will take alot of thinking just to be able to attain them! funny thing really i had just commented to other of my friends here on basically that self same topic about 10 minutes ago!! hope to hear more from you too! thank you very much…george scaglione

Charter

In Centauri Dreams, Paul Gilster looks at peer-reviewed research on deep space exploration, with an eye toward interstellar possibilities. For the last seven years, this site has coordinated its efforts with the Tau Zero Foundation, and now serves as the Foundation's news forum. In the logo above, the leftmost star is Alpha Centauri, a triple system closer than any other star, and a primary target for early interstellar probes. To its right is Beta Centauri (not a part of the Alpha Centauri system), with Beta, Gamma, Delta and Epsilon Crucis, stars in the Southern Cross, visible at the far right (image: Marco Lorenzi).

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